Stabilizing two-dimensional turbulent Kolmogorov flow via selective modification of inviscid invariants

We devise a methodology to stabilize two-dimensional turbulent Kolmogorov flow by carefully adjusting the rates of change of inviscid invariants, particularly energy, and enstrophy. Our technique automatically incorporates additional forces into the primary governing equation of the flow. This adjustment leads to a change in the way energy and enstrophy evolve over time, effectively guiding the turbulent flow to reach a stable state with a steady-state control input. When we remove the added control term, the flow moves closer to this invariant solution of Kolmogorov flow. The stable states serve as effective initial points for finding equilibrium solutions of the flow using Newton's method. This research presents a significant advancement in our ability to control and manipulate turbulent flow dynamics.